Eleven-year-old Sophia Ceballos, mom Catalina Robledo and their French bulldog Kokito boarded the flight Monday at Bush Intercontinental Airport. They claim they were forced to put his bag in the overhead compartment, and when the plane landed at LaGuardia Airport, Sophia says she and her mother made the heartbreaking discovery.

"She's like, 'He died, he died. Kokito, Kokito.' And he didn't wake up," Ceballos said. "She hit his chest so he could breathe, but he couldn't breathe."

A passenger posted on Facebook saying a flight attendant "insisted" the dog be placed in the compartment.

"They assured the safety of the family's pet," June Lara wrote. "So wearily, the mother agreed."

There are differing stories about whether or not the flight attendant knew a dog was in the carrier. Passenger Maggie Gremminger told ABC News that the flight attendant seemed shocked and frazzled to discover the animal and said if she had known, she never would have instructed it to be put in the bin above.

Ceballos and her mother insist that the flight attendant knew, saying that Kokito barked.

"While we were flying, the dog started barking and barking, and there was no flight attendants coming," Ceballos said. "We couldn't stand up because there was a lot of turbulence, so we weren't allowed to."

The family claims they told the flight attendant several times that their puppy was in the bag.

"She said, 'Oh, I'm sorry. I didn't know it was a dog. I thought it was a normal bag,'" Ceballos said. "But we told her it was a dog. She's lying."

Ceballos said the flight attendant made them store the bag above because it partially blocked the aisle.

"We were going to put him under the seat, and then the flight attendants came," Ceballos said. "She said, 'You have to put him up there because it's going to block that path.' And we're like, 'It's a dog. It's a dog.' She's like, 'It doesn't matter, you still put it up there.' And she just put, she helped her put it up, and she just closed it like it was a baggage."

The family described Kokito as a special, smart and sweet dog who loved to play around in parks. They said they are truly heartbroken.

"He was a member of our family," Ceballos said. "He was like my little brother to me."

United Airlines said in a statement to ABC News that it takes full responsibility and that pets should never be placed in the overhead bins.

United Airlines statement:

"This was a tragic accident that should never have occurred, as pets should never be placed in the overhead bin. We assume full responsibility for this tragedy and express our deepest condolences to the family and are committed to supporting them. We are thoroughly investigating what occurred to prevent this from ever happening again."

United didn't say whether anyone has been disciplined. The airline refunded the family's fare plus the fee for taking the pet on the plane.

Robledo said United called her asking to settle the situation with money. However, she says this isn't about money.

Other passengers took photos of the moments right after the flight landed, showing the distraught family.

According to Department of Transportation statistics on animal incidents on U.S. carriers, United has the highest rate of incidents involving loss, injury or death of animals during air transportation, with 2.24 incidents every 10,000 animals transported.